MomTrunc (version 5.97)

dprmvST: Multivariate Skew t Density, Probablilities and Random Deviates Generator

Description

These functions provide the density function, probabilities and a random number generator for the multivariate skew t (EST) distribution with mean vector mu, scale matrix Sigma, skewness parameter lambda and degrees of freedom nu.

Usage

dmvST(x,mu=rep(0,length(lambda)),Sigma=diag(length(lambda)),lambda,nu)
pmvST(lower = rep(-Inf,length(lambda)),upper=rep(Inf,length(lambda)),
        mu = rep(0,length(lambda)),Sigma,lambda,nu,log2 = FALSE)
rmvST(n,mu=rep(0,length(lambda)),Sigma=diag(length(lambda)),lambda,nu)

Arguments

x

vector or matrix of quantiles. If x is a matrix, each row is taken to be a quantile.

n

number of observations.

lower

the vector of lower limits of length \(p\).

upper

the vector of upper limits of length \(p\).

mu

a numeric vector of length \(p\) representing the location parameter.

Sigma

a numeric positive definite matrix with dimension \(p\)x\(p\) representing the scale parameter.

lambda

a numeric vector of length \(p\) representing the skewness parameter for ST and EST cases. If lambda == 0, the EST/ST reduces to a t (symmetric) distribution.

nu

It represents the degrees of freedom of the Student's t-distribution.

log2

a boolean variable, indicating if the log2 result should be returned. This is useful when the true probability is too small for the machine precision.

References

Cao, J., Genton, M. G., Keyes, D. E., & Turkiyyah, G. M. (2019) "Exploiting Low Rank Covariance Structures for Computing High-Dimensional Normal and Student- t Probabilities" <https://marcgenton.github.io/2019.CGKT.manuscript.pdf>.

Galarza C.E., Matos L.A., Dey D.K. & Lachos V.H. (2019) On Moments of Folded and Truncated Multivariate Extended Skew-Normal Distributions. Technical report. ID 19-14. University of Connecticut <https://stat.uconn.edu/tech-reports-2019/>.

Genz, A., "Numerical computation of multivariate normal probabilities," Journal of Computational and Graphical Statistics, 1, 141-149 (1992) <doi:10.1080/10618600.1992.10477010>.

See Also

dmvST, pmvST, rmvST, meanvarFMD,meanvarTMD,momentsTMD

Examples

# NOT RUN {
#Univariate case
dmvST(x = -1,mu = 2,Sigma = 5,lambda = -2,nu=4)
rmvST(n = 100,mu = 2,Sigma = 5,lambda = -2,nu=4)
#Multivariate case
mu = c(0.1,0.2,0.3,0.4)
Sigma = matrix(data = c(1,0.2,0.3,0.1,0.2,1,0.4,-0.1,0.3,0.4,1,0.2,0.1,-0.1,0.2,1),
               nrow = length(mu),ncol = length(mu),byrow = TRUE)
lambda = c(-2,0,1,2)
#One observation
dmvST(x = c(-2,-1,0,1),mu,Sigma,lambda,nu=4)
rmvST(n = 100,mu,Sigma,lambda,nu=4)
#Many observations as matrix
x = matrix(rnorm(4*10),ncol = 4,byrow = TRUE)
dmvST(x = x,mu,Sigma,lambda,nu=4)

lower = rep(-Inf,4)
upper = c(-1,0,2,5)
pmvST(lower,upper,mu,Sigma,lambda,nu=4)
# }